Anti-synchronized collective rotation in magnetic colloidal particles under rotating magnetic fields
Collective synchronization is a common response of interacting magnetic particles subjected to rotating external fields. Here we demonstrate a distinct nonequilibrium state in a two-dimensional cluster of magnetic colloidal particles in which the ordered crystalline core rotates, on average, opposite to the direction of the applied rotating magnetic field, while the defect-rich outer region continues to rotate with the drive. We term this state anti-synchronized collective rotation. By combining structural, spectral, bond-resolved, and layer-resolved torque analyses, we show that anti-synchronization is associated with a broader defect-rich interface, enhanced and dynamically heterogeneous bond deformation, and a reorganization of torque transmission between the surface and the crystalline interior. In the synchronized state, steric torques compensate the opposing dipolar contribution in the outer core, maintaining a positive net interaction torque. In the anti-synchronized state this compensation becomes insufficient, producing a negative net torque in theouter core and enabling core-surface rotational decoupling. Increasing the driving frequency restores coherent rotation through a transition characterized by competing positive- and negative-angular-velocity populations and hysteresis, consistent with a discontinuous, first-order-like dynamical transition. These results demonstrate how deformation and spatial redistribution of interaction torques can generate counter-rotating collective states in driven colloidal matter.